Slideshow has its own DockedCell so while you could do as you suggested it would require you to create your own stylesheet that adds the switching buttons to your docked cell and preserves the existing slideshow DockedCell.
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Mike HoneychurchJun 26 '12 at 7:01

@Vitaliy Kaurov, How do you get the broken egdes shown in your post?I'm fond of that.
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yulinlinyuJun 27 '12 at 2:18

into the options inspector. I just tried this and it works fine -- hopefully there are no unintended consequences so use at your own risk. :)

Edit

When I wrote this answer I chose "s" and "w" keys for "slideshow" and "working" just for example. Clearly it is not practical to tie up the "s" and "w" keys at the notebook level. However the next day I tried to make these event keys function keys and couldn't get it to work so contacted WRI tech support. They advise that there is no (documented) way to use the shift, option, control, and function keys with EventHandler. Further they said there is no way to use key combinations with EventHandler.

So therefore the stylesheet method that I posted the other day looks like the best way to (practically) achieve what you want.

You could edit the MenuSetup.tr file in the same manner as KeyEventTranslations.tr to include shortcut keys for each mode.

At present I cannot see a way to make this actually work. I am leaving the answer here for a while in case someone else can, and because I am curious to know what can be done with the "MenuListScreenStyleEnvironments" token.

+1 This is nice idea, thank you. I'd like to see also if someone will come up with button idea.
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Vitaliy KaurovJun 26 '12 at 6:05

@Vitaliy wait! I cannot find the menu items in MenuSetup.tr only a cryptic: MenuItem["Styles", "MenuListScreenStyleEnvironments", MenuAnchor->True]This method may not work.
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Mr.Wizard♦Jun 26 '12 at 6:06

Yes, it'd be good to check ;-) Maybe it'll still work out.
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Vitaliy KaurovJun 26 '12 at 6:08

@Vitaliy do you have any idea how to use these "MenuList..." items? There are a number of them in MenuSetup.tr and I don't know if it is possible to use these to drill down to find tokens for individual implicit sub-items.
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Mr.Wizard♦Jun 26 '12 at 6:21

Firstly make the docked cell grid. I'm using PaneSelector rather than If to choose how to layout the docked cell. An alternative is to create two separate docked cells, one for working and one for slideshow. This seems easier.

Yes I have deliberately removed the default docked cell. I wanted one docked cell for both environments. You don't need the slideshow forward and back, first & last controls for working environment. I'll leave it up to you to make two different docked calls. To keep the existing one for slideshow you will need to overlay it with the switching button and make that layer active.
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Mike HoneychurchJul 1 '12 at 4:01

For something really straightforward, could you not just use the built-in Slide Show palette? It has a View Environment button that allows you to select Slide Show, Working, Presentation, etc., from a drop-down list.

Of course this is not appropriate if you want your slide show view to be full-screen. But if you're toggling between slide show and working, it's likely this is something you might be doing during development of your notebook rather than during its presentation to an audience.

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